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Particle Morphology and Lithium Segregation to Surfaces of the LiLaZrO Solid Electrolyte 7

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Pieremanuele Canepa, James A. Dawson, Gopalakrishnan Sai Gautam, Joel M Statham, Stephen C Parker, and M. Saiful Islam Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b00649 • Publication Date (Web): 12 Apr 2018 Downloaded from http://pubs.acs.org on April 12, 2018

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Chemistry of Materials

Particle Morphology and Lithium Segregation to Surfaces of the Li7La3Zr2O12 Solid Electrolyte Pieremanuele Canepa,∗,† James A. Dawson,† Gopalakrishnan Sai Gautam,‡ Joel M. Statham,† Stephen C. Parker,† and M. Saiful Islam∗,† †Department of Chemistry, University of Bath, Bath, BA2 7AY, UK ‡Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA E-mail: [email protected]; [email protected]

Abstract Solid electrolytes for solid-state Li-ion batteries are stimulating considerable interest for next-generation energy storage applications. The Li7 La3 Zr2 O12 garnet-type solid electrolyte has received appreciable attention as a result of its high ionic conductivity. However, several challenges for the successful application of solid-state devices based on Li7 La3 Zr2 O12 remain, such as dendrite formation and maintaining physical contact at interfaces over many Li intercalation/extraction cycles. Here, we apply first-principles density functional theory to provide insights into the Li7 La3 Zr2 O12 particle morphology under various physical and chemical conditions. Our findings indicate Li segregation at the surfaces, suggesting Li-rich grain boundaries at typical synthesis and sintering conditions. On the basis of our results, we propose practical strategies to curb Li segregation at the Li7 La3 Zr2 O12 interfaces. This approach can be extended to other Li-ion conductors for the design of practical energy storage devices.

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Introduction The commercial Li-ion battery, which relies on liquid electrolytes, is now the workhorse behind the mobile electronics industry. 1–5 Unfortunately, a practical limit of what can be achieved with the current Li-ion technology is encountered when the focus shifts to electric vehicles. 2,4–6 One promising avenue to improve the energy and power densities of Li-ion batteries, while enhancing their safety, consists of replacing the flammable liquid electrolyte with a solid electrolyte capable of efficiently shuttling Li ions between electrodes. 7–21 To facilitate this transition, the Li-ion conductivity of solid electrolytes must be competitive to that of their liquid analogs. 12,16 While significant attention is still devoted to intrinsic Li+ conductivity in solid electrolytes, many challenges remain for future solid-state applications. 5,22–30 The most pressing challenges are finding solid electrolytes that are electrochemically stable against electrodes, maintaining physical contact between components over many Li intercalation/extraction cycles and suppressing Li-dendrite formation. The Li7 La3 Zr2 O12 garnet-type electrolyte has received significant attention due to its high ionic conductivity (10−6 –10−3 S cm−1 ) achieved by a variety of doping strategies, 7,8,10,11,31–36 but most importantly because of its perceived stability against the Li-metal anode. 25,27,29,37–41 However, the failure of polycrystalline Li7 La3 Zr2 O12 in solid-state battery prototypes comprised of Li-metal anodes has been the subject of several studies. 25,28,38,40–43 It has been observed 29 that once Li fills a crack in Li6 La3 ZrTaO12 , fresh electro-deposited Li is extruded to the available surface. Tests with Li-metal/Li7 La3 Zr2 O12 /Li-metal cells showed that only small current densities of ∼ 0.5 mA cm−2 could be tolerated before dendrite failure. 27,44 Rationalising the mechanisms behind the propagation of dendrites in Li7 La3 Zr2 O12 is a major challenge. In parallel, sintering strategies to maximise the bulk transport in ceramic materials are routinely applied. While high temperature densification enhances ion transport, the extent of morphological transformations of the electrolyte particles is still unclear. Kerman et al. 27 highlighted the connection between the processing conditions of Li7 La3 Zr2 O12 and its particle 2


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morphology and size. Kingon et al. 45 demonstrated that ceramics containing volatile cations, such as Li7 La3 Zr2 O12 , become Li deficient upon sintering. These experimental observations indicate that it is crucial to understand the variation of the Li7 La3 Zr2 O12 morphology as a function of chemical and physical properties (composition and temperature). In this study, we develop a phenomenological model based on first-principles calculations to determine the composition of Li7 La3 Zr2 O12 particles, while the chemical environment of Li, La, Zr and O, voltage and/or the temperature are varied. Rationalising the particle morphology of solid electrolytes contributes towards a deeper understanding of several critical phenomena, including the Li+ conductivity at grain boundaries and the propagation of dendrites during battery operation. Indeed, our results predict significant Li accumulation at the exterior of the Li7 La3 Zr2 O12 particles when we mimic reducing high-temperature synthesis conditions. Based on our computational insights, we propose practical strategies to engineer the chemical compositions of the particles, providing a greater control of the complex chemistry of Li7 La3 Zr2 O12 . These general design strategies can be extended to other solid electrolytes and electrode materials.

Results Phase stability and chemical domains We first consider the relative stability of the Li7 La3 Zr2 O12 tetragonal (space group I41 /acd) ¯ polymorphs. The computed lattice constants (a = 13.204 and high-temperature cubic (Ia3d) and c = 12.704 ˚ A) of the tetragonal phase compare well with the experimental data (a = 13.134 and c = 12.663 ˚ A). 46 Figure 1a shows the decomposition of Li7 La3 Zr2 O12 into Li6 Zr2 O7 + La2 O3 + Li8 ZrO6 , revealing the metastability of both the cubic (∼ 22 meV/atom above the stability line at 0 K) and tetragonal (∼ 7 meV/atom) polymorphs, in agreement with 3



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previous density functional theory (DFT) preditions. 47,48 a

La2O3

O2

b

ZrO2

Li2ZrO3 Li6Zr2O7

O6

L

r i 8Z

Zr

Li7La3Zr2O12 Li2O

Li7La3Zr2O12

Li6Zr2O7

La2O3

Figure 1: (a) La2 O3 –Li6 Zr2 O7 -Li8 ZrO6 projection of the quaternary Li–La–O–Zr phase diagram showing the decomposition products of the metastable Li7 La3 Zr2 O12 (blue diamond), which are Li6 Zr2 O7 , La2 O3 and Li8 ZrO6 . (b) Compound Li2 O–La2 O3 –Zr–O2 phase diagrams where Li7 La3 Zr2 O12 is assumed to be stable. Green dots display the stable phases, while red, blue and grey lines identify equilibrium tie lines. Dash blue lines mark tie lines shared by Li7 La3 Zr2 O12 and some of the binary precursors used in its synthesis. Both phase diagrams are computed from DFT data at 0 K and combined with existing entries in the Materials Project database. 49 The degree of metastability of the tetragonal phase is small enough that the compound can be stabilised by thermal effects, which explains the success of high-temperature (> 600 ◦

C) phase-pure synthesis. 8,11 It is assumed that the chemical decomposition of Li7 La3 Zr2 O12

into Li6 Zr2 O7 + La2 O3 + Li8 ZrO6 requires a major coordination rearrangement of Zr and La, thereby kinetically preventing Li7 La3 Zr2 O12 from decomposing. Therefore, we assume that Li7 La3 Zr2 O12 is thermodynamically stable (see phase diagram in Figure 1b). Identifying the phases in equilibrium with Li7 La3 Zr2 O12 (Figure 1b) allows us to set the bounds of chemical potentials of each element, thus providing a thermodynamic framework to calculate meaningful non-stoichiometric surface energies (see Method section). Figure 1b illustrates the phases in equilibrium with Li7 La3 Zr2 O12 , which show that only La2 O3 , 4


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Li6 Zr2 O7 , Li2 O, O2 and Zr are in direct equilibrium with the solid electrolyte. Experimentally, the binary compounds La2 O3 , Li2 CO3 (LiOH or Li2 O) 29 and ZrO2 are used as precursors for the synthesis of Li7 La3 Zr2 O12 . 8,29 In addition, when Li7 La3 Zr2 O12 is assumed to be stable, Li8 ZrO6 becomes metastable in the Li-La-Zr-O phase diagram (Figure 1b). Our discussion moves to the definition of the relevant chemical potentials, which have to be rigorously defined to accurately calculate the energies of non-stoichiometric surface structures (see Eq. 1). From thermodynamic arguments, any combination of three compounds in equilibrium with Li7 La3 Zr2 O12 define distinct chemical potentials (µ) for the elements O, La, Li and Zr. In this study, we consider two different chemical regimes, i.e. oxidising and reducing. The tetrahedron composed of Li7 La3 Zr2 O12 , La2 O3 , Li2 O and O2 mimics the oxidising and experimental synthesis conditions of Li7 La3 Zr2 O12 . In contrast, we consider a reducing environment as defined by Li7 La3 Zr2 O12 being in equilibrium with Zr metal, La2 O3 and Li2 O, which corresponds to experimental sintering conditions. A detailed derivation and the bounds of the chemical potential used for each species are summarised in Section 1 and Table S1 of the Supplementary Information (SI). Although Zr forms oxides with multiple oxidation states, such as ZrO and Zr2 O as reported by Chen et al., 50 Zr is not redox active in Li7 La3 Zr2 O12 . Therefore, Zr-metal and ZrO2 represent valid reference states for the µZr in reducing (Zr0 ) and oxidising (Zr4+ ) environments, respectively.

Surface structures and energies Surfaces of solid electrolytes are important to their electrochemical properties, particularly due to the presence of active interfaces within intercalation batteries. The Li7 La3 Zr2 O12 cubic polymorph provides the highest ionic conductivity. 11,47,51 However, accounting for the Li disorder presents a major computational complexity when creating representative surface structures. Thus, we consider the tetragonal polymorph, which constitutes a distinct ordering of Li sites, as the reference structure for creating our surface models. 5



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Figure 2 depicts the atomic arrangement of the Li-terminated (010) surface of Li7 La3 Zr2 O12 , highlighting the significant reconstruction of the Li and O layers, respectively. The dotted

O

[010]

Li

Zr La

Surface region Bulk-like region

z Figure 2: Sideview of the non-stoichiometric (010) Li-terminated surface of Li7 La3 Zr2 O12 . Li atoms are in red, O in green, La in blue and Zr in gold. Solid lines identify the arrangement of each atom plane along the non-periodic z axis. The black line marks the separation between the bulk-like region from the surface region. The black dotted lines are guides for the eye to highlight the change in the local Li symmetry upon surface reconstruction. lines in Figure 2 are a guide for the eye to illustrate the loss of symmetry of the Li environment at the surface compared to the bulk region. Figure 2 shows that La layers overlap with “rumpled” oxygen layers, which contribute to stabilise La-terminated surfaces, as discussed in the following paragraphs. In the case of Zr ions, the oxygen coordination environment in the surface slab show insignificant deviation from the octahedral coordination within bulk Li7 La3 Zr2 O12 , in qualitative agreement with the lack of surface reconstruction observed in 6


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ZrO2 . 52 It is known that for a given Miller index several surface terminations may be possible since the bulk can be cleaved at different planes, as shown in Figure 2. The relative stability of each surface model is defined by their surface energy (γ, Eq. 1). Figure 3 depicts the computed γ values of a number of stoichiometric and non-stoichiometric La, Li, O and Zrterminated surfaces of Li7 La3 Zr2 O12 . Non-stoichiometric surfaces refer to surfaces where the stoichiometry deviates in composition from the bulk. The surface energies of symmetryrelated Miller index surfaces (e.g., (100) ≈ (010) ≈ (001)) are detailed in Table S2. As introduced in Section , the chemical potentials, µi , for calculating γ of non-stoichiometric surfaces are set to reducing conditions (i.e., µLa ≈ µLa in La2 O3 , µLi ≈ µLi in Li2 O, and µZr ≈ µZr in Zr metal), see Figure 1b and Section 1 of the SI.

γ (J m–2)

Li–terminated (021)

O–terminated 1.8 1.6 1.4 1.2

(111)

1.0 0.8

(110) (010)

(110) (010)

(110)

(010) (010) (110)

(021)

La–terminated

Zr–terminated

Figure 3: Surface energies γ (J m−2 ) of La (blue), Li (red), O (green) and Zr (yellow) -terminated surfaces of Li7 La3 Zr2 O12 . Hatched bars indicate non-stoichiometric surfaces, whose surface energies are derived using the chemical potentials from Figure 1b. The chemical potentials of Li, La and Zr are fixed by Li2 O, La2 O3 and Zr metal, respectively, corresponding to reducing conditions (details in Section ). 7



Figure 3 shows three main features: i) Zr-terminated surfaces show the highest surface energy γ (> 1.5 J m−2 ), ii) certain Li-terminated surfaces possess significantly lower γ (∼ 0.87±0.02 J m−2 for the (010) surface), in good agreement with previous work. 48 iii) La- and O-terminated surfaces show similar surface energies, as indicated by γ 0.98 J m−2 and 0.99 J m−2 for the La- and O-terminated (110) surfaces, respectively. Although the surface structures are obtained from the tetragonal phase, we find identical surface energies for symmetry inequivalent surfaces (see Table S1 and Figure S1). For example, the surface energy (∼ 1.77 J m−2 ) of the Zr-terminated (010) surface is identical to the (001) and (100) surfaces, which is typically not found for tetragonal structures. This suggests the similarity between the tetragonal and cubic phases of Li7 La3 Zr2 O12 and indicates that the Li ordering, which affects the relative stability of the bulk tetragonal and cubic phases, has only a negligible impact on the relative symmetry and energetics of Li7 La3 Zr2 O12 surfaces. Notably, the c/a ratio exhibited by the tetragonal phase (∼ 0.96 from experimental lattice constants, see Section ) signifies the “small” tetragonal distortion in Li7 La3 Zr2 O12 .

Effects of oxygen environment and temperature on surfaces With the aim of understanding the interplay between compositional and temperature effects on the morphology of Li7 La3 Zr2 O12 , we now move our attention to trends of surface energy as a function of temperature and oxygen composition. To include temperature dependence in our model, we apply a thermodynamic framework (detailed in the Method section) that connects changes in the O2 chemical potential, µO2 , directly to temperature. 53 This approximation is valid as the Li7 La3 Zr2 O12 electrolyte is in contact with an oxygen environment during its synthesis and sintering. With µO = 21 µO2 , µO sets the surface energy of non-stoichiometric surfaces, as indicated in Eq. 2. Note that under both oxidising and reducing conditions (Section ), the chemical potentials of La and Li are set by La2 O3 and Li2 O, respectively. All the non-stoichiometric surfaces studied here are either oxygen rich or poor (see Method section). High µO (or µO2 ) 8


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represents low-temperature situations and a highly oxidative environment, where oxygen molecules “condense” on the surfaces of Li7 La3 Zr2 O12 . In contrast, higher temperatures (i.e., more negative µO ) signify reducing conditions, where oxygen atoms become volatile and leave the surface as O2 gas, which is equivalent to Li7 La3 Zr2 O12 being in equilibrium with Zr metal. Figure 4 shows the variation of the surface energy for a number of non-stoichiometric surfaces as a function of temperature, or its equivalent µO , corresponding to an oxygen partial pressure of 1 atm. A number of important observations can be drawn from Figure 4. i) The Li-terminated (010) surface has the lowest γ (as in Figure 3) and the La-terminated (010) stoichiometric surface has the highest γ for temperatures higher than 25 ◦ C. The negative slope of each line signifies that all the surfaces are oxygen deficient. While studying non-stoichiometric surfaces, we have focused on La, Li and O deficient scenarios, as they are most likely to develop at high temperatures. 54,55 In order to maintain the electroneutrality of oxygenterminated surfaces, oxygen vacancies were introduced to compensate the removal of cations (details are provided in the Method section). ii) The stability of the Li-terminated (010) surfaces in comparison to other terminations is significant. iii) At temperatures higher than 300 ◦ C, the O-terminated (010) and (110) surfaces become more stable than the (110) Li-terminated surface. This result is also found for the (100), (001), (011) and (101) Literminated facets. iv) Above 750 ◦ C, the negative γ of (010) Li-terminated surface (as seen in Figure 4) is indicative of the instability of bulk Li7 La3 Zr2 O12 , and may be linked to the melting of Li7 La3 Zr2 O12 particles.

Environment dependent particle morphologies By combining our surface energies of various surface facets at distinct chemical compositions (Figures 3 and 4), we can implement the Wulff construction to derive the Li7 La3 Zr2 O12 equilibrium particle morphology at synthesis conditions. 9



O2-rich (oxidising)

O2-poor (reducing)

O chemical potential µO

(J m 2)

1.2 1.0

Surface energy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.6

-0.25

-0.5

-0.75

(010) La stoichiometric

µ⇤O (eV)

-1.0

-1.25

-1.5

Synthesis and sintering regimes

0.8 (010

) La

(010) La sto (010) Li (010) La (010) O (110) Li (110) O

0.4 0.2 0.0 200

0

200

(11

0) L

i

(0

400

10 )

600

Temperature ( C)

Li

800 1000

Figure 4: Surface energy γ of La (blue), Li (red) and O (green) -terminated Li7 La3 Zr2 O12 surfaces vs temperature and oxygen chemical potential µO . The blue horizontal line indicates the stoichiometric La-terminated surface energy. The zero (eV) in the µO scale is normalised against the reference state µ∗O and is detailed in the SI. µO near 0 eV relates to oxygen-rich (or oxidising) regimes, whereas more negative oxygen chemical potentials are oxygen-poor (or reducing) conditions. The grey shading marks the experimental temperature window for synthesis and sintering of Li7 La3 Zr2 O12 . 11 The chemical potentials of Li and La are fixed by Li2 O and La2 O3 , respectively, while µO is allowed to vary. Figure 5 depicts the change of the particle equilibrium morphology as a function of temperature. At room temperature (∼ 24 ◦ C), the equilibrium Li7 La3 Zr2 O12 particle morphology is dominated by the (001), (101) and (110) surfaces. For temperatures greater than 600 ◦ C 10


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24 ℃

180 ℃

≥ 600℃ (010)

(010) (001)

(100)

(010)

(100)

(010)

(101)

(100) (110)

1 2 3 4 5 6 7 8 (010) 9 (001) 10(101) 11 12(110) 13(111) 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5: Variation in the Li7 La3 Zr2 O12 equilibrium morphology with increasing temperature. The particles are expected to be Li-terminated, as suggested in Figure 4. Labels identify the surface planes of interest. (and < 750 ◦ C), Li7 La3 Zr2 O12 particles should assume a cubic shape dominated by the (100) and (010) surfaces, as seen in Figure 5. At 24 ◦ C and intermediate temperatures (∼ 180 ◦ C), the (110) Li-terminated surface contributes to the overall particle shape. However, an increase in oxygen composition on the surface of the Li7 La3 Zr2 O12 particles will be also observed, as shown by the increased stability of the (110) oxygen-terminated surfaces over (110) Li-terminations, as seen in Figure 4 at temperatures above 300 ◦ C.

Tuning the synthesis conditions of Li7 La3 Zr2 O12 We now discuss the surface phase diagram obtained by varying the chemical composition of Li7 La3 Zr2 O12 . This analysis contributes to understanding the experimental synthesis conditions to achieve the desired chemical composition of the particle surfaces. Computing a complete surface phase diagram represents a formidable exercise given the large compositional space for the non-stoichiometric terminations accompanied by the large number of atomic arrangements of partially occupied terminating layers. Thus, we limit the discussion of the surface phase diagram to the Li7 La3 Zr2 O12 surfaces in Figure 3. Li-rich and Li-poor conditions correspond to Li2 O (reducing conditions) and Li6 Zr2 O7 (oxidising conditions), respectively, while Zr-rich is equivalent to Zr metal (reducing) and Zr-poor to 11



O2 gas (oxidising). Figure 6 shows the surface phase diagram at 0 K by varying the Li (µLi ) and Zr (µZr ) composition. We find that regions of low µLi and µZr are consistently dominated by the

Voltage vs Li/Li+ (V) 0.05 0.5 0

Li shell

1.0

1.5

2.0

2.5

3.0

O/La shell

−2 −4 −6 −8

Li7La3Zr2O12

(110) Li (010) Li

µ Zr - µ *Zr (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(010) O/La Li7La3Zr2O12

− 10

– 12 − 12 – 0.05− 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 3.0

Li-rich (reducing)

µ Li - µ *Li (eV)

Li-poor (oxidising)

Figure 6: Surface phase diagram at 0 K of Li7 La3 Zr2 O12 and schematic representations of particle morphologies at different chemical conditions. Stable surfaces and chemical terminations as a function of µLi and µZr . The white square identifies the compositional Li–Zr conditions where Li7 La3 Zr2 O12 is commonly synthesised. Zr-rich is equivalent to Zr metal (Zr-poor is O2 gas), whereas Li-rich is Li metal (and Li-poor is Li6 Zr2 O7 ). The voltage evolution vs Li/Li∗ (with V = −µLi · e− ) is also shown. The chemical potential scales are referenced against the reference states µ∗Li (Li2 O) and µ∗Zr (Zr metal). (010) O- and La-terminated surfaces. At more positive µLi and µZr (near Li-rich and Zrrich conditions), the (010) Li-terminated surfaces are stable. In fact, the (010) O- and La-terminated surfaces have similar surface energies ∼ 0.94 and ∼ 0.98 J m−2 , respectively (see Figure 3), as the La ions exposed are surrounded by a O sub-layer. The La/O or Li segregations at the surface of the particles of Li7 La3 Zr2 O12 (at specific µLi and µZr ) are

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schematically shown by the green and violet spheres of Figure 6. Figure 6 also includes a voltage scale, which relates directly to the Li chemical potential (V = −µLi · e− ). Negative µLi signify high voltages (vs Li/Li+ ) and vice versa.

Discussion To gain realistic insights into the design of solid electrolytes for solid-state batteries, we have performed a thorough first-principles calculation analysis of the Li7 La3 Zr2 O12 surfaces and its morphologies under various physical and chemical conditions. Morphology and composition of Li7 La3 Zr2 O12 particles – Figure 1b shows that lower surface energies are found for surfaces terminated by cations with lower oxidation states, following the trend Li+ < La3+ < Zr4+ . This finding relates to electrostatic and geometric factors. By cleaving a cation-terminated surface, the large disruption of the ideal cation coordination environment results in a high-energy penalty, thus impacting significantly the relative stability of the surface. Experimentally, 56 it is found that La3+ and Zr4+ ions prefer high oxygen coordination (≥ 6 in the cubic and tetragonal Li7 La3 Zr2 O12 phases), whereas Li+ can adjust to both octahedral and tetrahedral environments. 11,57 Li ions can tolerate reduced coordination environments leading to lower surface energies compared to Zr-terminated surfaces, which undergo a reduction in coordination from 6–8 to 4. La-terminated surfaces show low surface energies (∼ 0.94 J m−2 ) compared to the Zr-terminated surface, which are explained by the oxygen sub-layer stabilising the partially uncoordinated La atoms and lowering the surface energy (see Figure S3). We have identified that surfaces with low Miller indices, e.g. (010) and (110) with Lirich textures, dominate across a wide range of temperatures and oxygen environments. Li segregation at the surfaces of Li7 La3 Zr2 O12 particles has been demonstrated by neutron depth profiling experiments. 39 O-terminated surfaces are also possible, as shown in Figure 6. This

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may be significant in relation to the recent report of oxygen migration in Li7 La3 Zr2 O12 . 58 The predicted room temperature morphology of Li7 La3 Zr2 O12 is in excellent agreement with a scanning electron microscopy study of a single crystal, 46 providing credibility to the computed morphologies of Figure 5. However, no specific surface facets were characterised, which we identified here. 46 We can complement the experimental observations by extending our model beyond the shape of the particles. This is completed by ascertaining the dominant surface facets and the most likely chemical compositions under both reducing and oxidising conditions. On the basis of these findings we speculate that small cations, such as Al3+ and Ga3+ , doped at Li+ sites may segregate at the surfaces of the particles. In agreement with our hypothesis, a number of experimental reports demonstrate that Al3+ segregates to the grain boundaries of doped Li7 La3 Zr2 O12 . 55,59,60 We speculate that high-valent cations, such as Ta5+ and Bi5+ (introduced on the Zr lattice to increase the number of Li vacancies), 11 will constitute the core of the Li7 La3 Zr2 O12 particles.

Densification and implications on ionic conductivity – Densification of ceramic oxides via high-temperature (and spark-plasma) sintering is routinely employed to improve the electrolyte ionic conductivity. 11,45,55 Typically, the interpretation of impedance measurements requires the deconvolution of the total ionic conductivity into three main contributions, namely, 61–63 intrinsic bulk, grain boundary and interfacial electrolyte/blocking electrode. While bulk Li-ion transport has been emphasised by both experiment and computation, 7–9,11,31,32,47,51 grain boundary Li-ion conductivity is much less examined, despite being crucial. 7–9,11 The seminal paper on Li7 La3 Zr2 O12 by Murugan et al. 8 showed significant Li-ion resistance at the grain boundaries (∼ 50% of the total), thus suggesting the relevance of intergranular Li-ion transport. 64 Ceramic oxides processed at high temperatures containing “volatile” cations, such as Li, including Li7 La3 Zr2 O12 , will produce Li deficient bulk materi-

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als, 27 and thus possible Li loss upon sintering treatments. For example, Antolini 54 showed that sintering of Lix Ni1−x O ceramic electrodes can promote Li segregation at the particle exterior, thus altering the overall stoichiometry. Loss of Li2 O was observed in the synthesis of Li7 La3 Zr2 O12 , 35,36,55,65 and additional Li2 O is routinely added during its preparation. In agreement, our prediction in Figure 4 suggests that at high temperatures (≥ 600 ◦ C in the sintering regime) and reducing conditions, the particle surfaces will show pronounced segregation of Li. Assuming that the stable surfaces computed in this study are representative of the grain boundaries in Li7 La3 Zr2 O12 , we speculate that the accumulation of Li ions can impact the Li transport involving grain boundaries. 64

Engineering the particle morphology – On the basis of our predictions, we can propose practical strategies to engineer particle morphologies of Li7 La3 Zr2 O12 . For example, Figure 6 demonstrates that adding extra Zr and/or Li metals during synthesis may promote Li segregation at the grain boundaries. 39 In addition, as indicated in Figure 4, routine high-temperature synthesis of Li7 La3 Zr2 O12 promotes reducing conditions (i.e., oxygen-poor conditions) and Li terminated surfaces/particles. Hence low-temperature synthesis (and sintering) protocols should be sought. 66 From analysis of Figure 6, we speculate that O/La accumulation at the grains is also observed near the operating voltages of typical Li-ion cathode materials (e.g., LiCoO2 ∼ 3.8 V vs. Li/Li+ and LiFePO4 ∼ 3.4 V). In this context, Miara et al. 67 have shown that Li7 La3 Zr2 O12 remains stable against LiCoO2 , whereas the analogous interface with LiFePO4 decomposes forming a protecting Li3 PO4 interface. Nevertheless, a more recent experimental investigation by Goodenough et al., 68 showed significant Al3+ and La3+ migration from Al-doped Li7 La3 Zr2 O12 to LiCoO2 , and negligible Zr diffusion into LiCoO2 . In Figure 6, near 3 V we predict La segregation towards the particle surfaces corroborating these experimental findings. The failure upon short-circuiting of polycrystalline Li7 La3 Zr2 O12 in solid-state devices,

15



utilising a Li-metal anode, has been linked to dendrite propagation. 27 Near 0 V or at the potential of Li metal, we expect the Li7 La3 Zr2 O12 particles to be lithium terminated. In agreement with our results, Li segregation close to a Li-metal anode interface in Al-doped Li7 La3 Zr2 O12 has been recently observed by in situ transmission electron microscopy. 38 We speculate that the occurrence of Li at the particle surface and at grain boundaries, could indeed set the ideal chemical environment required for Li-dendrite growth and propagation between Li7 La3 Zr2 O12 particles. In line with our results, Kerman et al. 27 proposed that once Li fills a crack in doped Li7 La3 Zr2 O12 , fresh electrodeposited Li extrudes to the existing grain boundaries. Unsurprisingly, the process of dendrite propagation can originate from Li “stuffing” into grain boundaries. 27 Thus, the significant accumulation of Li at the surfaces of the Li7 La3 Zr2 O12 particles may favour the initial stages of dendrite nucleation and growth along the existing grain boundaries. Further experimental studies are required to verify these hypotheses.

Conclusions Li7 La3 Zr2 O12 is an important solid electrolyte material, but its surfaces and particle morphologies under synthesis and sintering conditions are not fully characterised. First, by studying the morphology and composition of Li7 La3 Zr2 O12 particles from DFTbased calculations, we have demonstrated the spontaneous segregation of Li towards the particle exterior. Second, we map the compositional changes of the surfaces of Li7 La3 Zr2 O12 as a function of temperature and of oxygen chemical pressure. Li segregation to surfaces is the dominant process over a range of temperatures, particularly during high-temperature synthesis and sintering. These findings are significant in relation to the initial stages of Li dendrite growth. Third, by studying the surface phase diagram of Li7 La3 Zr2 O12 , we find that Li segregation can be curbed by tuning the ceramic synthesis conditions. We show that

16


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synthesis in reducing environments (O-poor, Li-rich and/or Zr-rich) may promote Li segregation to the particle surfaces. Finally, we find that particle compositions of Li7 La3 Zr2 O12 are altered upon voltage sweeps, with Li segregation at the exterior occurring at the Li-metal anode voltage. These findings will contribute towards developing strategies for the optimisation of the synthesis and operation of promising solid electrolytes for solid-state batteries.

Method Surface energies and thermodynamic framework The physical quantity defining stable surface compositions and geometries is the surface free energy γ (in J m−2 ): " # species X 1 Gsurface − Gbulk − ∆ni µi γ= 2A i

(1)

where A is the surface area (in m−2 ) and Gsurface and Gbulk are the surface free energies of periodic surfaces and the reference bulk material, respectively. Gsurface and Gbulk are approximated by the respective computed internal energies Esurface and Ebulk , accessed by density functional theory (DFT) as described in the SI. In the case of non-stoichiometric surfaces, the final surface energy depends on the environment set by the chemical potential µi for species i and amounting to an off-stoichiometry of ∆ni . Note that ∆ni is negative (positive) if species i is removed (added) to the surface. The chemical potential references µi were derived from the computed phase diagram (Figure 1b) at 0 K. Eq. 1 provides γ values at 0 K that are not representative for the operating conditions of solid electrolytes and the synthesis and sintering conditions. For non-stoichiometric surfaces, the approximation chosen to introduce the temperature dependence in the γ values is based on the fact that the surrounding O2 atmosphere forms an ideal-gas-like reservoir, which is in equilibrium with Li7 La3 Zr2 O12 . The effect of temperature is introduced into the definition

17



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of γ as follows:  γ(T ) =

1  Esurface − Ebulk − 2A



species−{O}

X i

∆ni µi − ∆nO µO (T )

(2)

where µO is now a temperature dependent quantity and evaluated directly by combining DFT data with experimental values tabulated by NIST/JANAF as: 69

µO (T )= 12 µO2 (0 K,DFT)+ 21 µO2 (0 K,Exp.)+ 12 ∆GO2 (∆T,Exp.)

(3)

where the µO2 (0 K, DFT) is the 0 K free energy of an isolated oxygen molecule evaluated with DFT, whereas µO2 (0 K, Exp.) is the 0 K experimental (tabulated) Gibbs energy for oxygen gas. ∆GO2 (∆T, Exp.) is the difference in the Gibbs energy defined at temperature, T , as 1/2[H(T, O2 ) − H(0 K, O2 )] − 1/2T [S(T, O2 )], respectively, as available in the NIST/JANAF tables. 69 We omitted the partial pressure dependence of the µO2 term (i.e., we used pO2 = 1 atm) as we expect this contribution to be small, as demonstrated previously. 53

Bulk surface models Because of the large number of possible chemical terminations, as a result of the quaternary nature of Li7 La3 Zr2 O12 , the selection of surfaces investigated was only limited to low-index surfaces, such as (100), (001), (101), (111) and (201). We note that some of these surfaces are related by the intrinsic tetragonal symmetry. For example, (100) = (010), as verified by the surface energies in the Supplementary Information (see Table S2). In line with Tasker’s classification of oxide surfaces, 70 only realistic type I surfaces were considered, which are characterised by zero charge and no electrical dipole moment. Nevertheless, these requirements are only satisfied by a limited number of stoichiometric Zr- or La-terminated surfaces with high surface energies. Because our goal is to rationalise the chemical composition and morphology of the

18


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Li7 La3 Zr2 O12 particles, it is crucial to study the Li- and O-terminated surfaces. As a result, type I non-stoichiometric surfaces were generated by selectively removing layers of Zr and/or La and charge-compensated by O removal, as shown schematically in Figure 2. Upon cation removal, charge neutrally is maintained by introducing oxygen vacancies, resulting in the need to investigate a significant number of atomic orderings. We simplify this difficult task by computing with DFT only the 20 orderings with the lowest electrostatic energy, as obtained by minimising the Ewald energy of each surface using formal charges. 71 This results in the assessment of 420 non-stoichiometric surfaces using DFT. While performing this operation, we enforce symmetry between the two faces of the surfaces. Using this strategy, we identified 21 non-stoichiometric orderings and 11 stoichiometric surfaces that are O-, Li-, La- and Zr-terminated, respectively, whose surface energies are discussed in Figure 3 and Table S2.

Acknowledgements The authors gratefully acknowledge the EPSRC Programme Grant (EP/M009521/1) and the MCC/Archer consortium (EP/L000202/1). PC is grateful to the Ramsey Memorial Trust and University of Bath for the provision of his Ramsey Fellowship. PC is thankful to Dr. Benjamin Morgan at the University of Bath for fruitful discussions. PC deeply indebted to Dr. yet to be Theodosios Famprikis at the LRCS, Amiens, France. We acknowledge fruitful discussion with Prof. Peter Bruce, Stefanie Zekoll and Dr. Jitti Kasemchainan at the University of Oxford.

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website at DOI:

19



• Details of first-principles calculations. • Chemical potentials bounds. • Surface energies. • Li7 La3 Zr2 O12 particle morphologies. • Li7 La3 Zr2 O12 surface reconstruction.

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O chemical potential µO 1.2

Page 29 of 29

(J m 2)

1.0

Surface energy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

0.6

-0.25

-0.5

-0.75

µ⇤O (eV)

-1.0

-1.25


-1.5

Synthesis and sintering regimes

(010) La

Li (010)

0.8 (010

) La

(010) La sto (010) Li (010) La (010) O (110) Li (110) O

0.4 0.2 0.0 200

0

200

(11

0)

(0

Li

10

)L

i

400

600

Temperature ( C)

800 1000


Li7La3Zr2O12

Particle Morphology and Lithium Segregation to ... - ACS Publications

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